Lectures related to Riemann Integral: Subdivisions and Volumes

Restriction, Prolongement et Graphe d'une Fonction

Explains the relationship between two functions through restriction and prolongation, emphasizing the importance of defining a function by its graph.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Graphical Definition: Level Sets and Domains

Covers the graphical definition of functions, focusing on level sets and domains.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.

Mathematical Analysis: Functions and Composition

Covers the analysis of functions, composition, and mathematical induction.

Integral Calculus: Riemann Integration

Explores Riemann integration for functions of several variables, Darboux sums, and the criteria for integrability.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Optimal Transport: Cyclically Monotone Sets

Covers cyclically monotone sets in optimal transport theory and their properties.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Counterfactuals: SEM and D-Separation

Explores counterfactuals in SEMs and D-Separation in graphical models.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

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Advanced Analysis II: Tangent Plan and Differentiability

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Functions and Integers

Covers functions, integers, GCD, and reasoning by recurrence, including the Euclidean algorithm and induction principle.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Graph and Diagonal

Discusses the graph of a relation and the concept of separation.